Calculus 10th Edition

by
Larson, Ron; Edwards, Bruce H.

Published by
Brooks Cole

ISBN 10:
1-28505-709-0

ISBN 13:
978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.5 Exercises: 23

Answer

No vertical asymptotes.

Work Step by Step

$f(x)=\dfrac{x^2-2x-15}{x^3-5x^2+x-5}=\dfrac{(x-5)(x+3)}{(x-5)(x^2+1)}=\dfrac{x+3}{x^2+1}.$
Vertical asymptotes occur when the denominator alone is $0\to$
$x^2+1=0\to x^2=-1$ which has no real solution, hence the function has no vertical asymptotes.